exponential smoothing vruchtensappen - sanne peelmans

R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 12:57:14 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/27/t12119146949n46bgk44o210o5.htm/, Retrieved Tue, 27 May 2008 20:58:18 +0200

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Dataseries X:

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1,08 1,08 1,09 1,1 1,1 1,11 1,1 1,1 1,11 1,11 1,11 1,11 1,11 1,12 1,11 1,11 1,12 1,12 1,11 1,12 1,11 1,11 1,1 1,1 1,1 1,11 1,1 1,1 1,09 1,1 1,1 1,11 1,13 1,13 1,13 1,13 1,14 1,14 1,14 1,15 1,15 1,15 1,15 1,15 1,15 1,14 1,14 1,14 1,13 1,12 1,13 1,13 1,13 1,12 1,13 1,12 1,12 1,11 1,11 1,11 1,11 1,14 1,15 1,15 1,16 1,15 1,16 1,13 1,13 1,12 1,12 1,11 1,11

Text written by user:

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.725335875539957 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.11 1.10716184850511 0.00283815149489031 14 1.12 1.11795589554655 0.00204410445344738 15 1.11 1.10861314888205 0.00138685111795045 16 1.11 1.10961908175193 0.000380918248068518 17 1.12 1.12031371194296 -0.000313711942956596 18 1.12 1.12092549562627 -0.000925495626272976 19 1.11 1.11108451567403 -0.00108451567403356 20 1.12 1.12114131201974 -0.00114131201973899 21 1.11 1.11114455815405 -0.00114455815404702 22 1.11 1.11114887817193 -0.00114887817192821 23 1.1 1.10196918656044 -0.00196918656044298 24 1.1 1.10261579111840 -0.00261579111840238 25 1.1 1.10525415369942 -0.00525415369941795 26 1.11 1.10989406809700 0.00010593190299657 27 1.1 1.09906318237804 0.000936817621960628 28 1.1 1.09946892351297 0.000531076487026549 29 1.09 1.10998817743964 -0.0199881774396358 30 1.1 1.09614649088951 0.00385350911049098 31 1.1 1.08990124146048 0.0100987585395207 32 1.11 1.10792923329356 0.00207076670644013 33 1.13 1.10034772091048 0.0296522790895171 34 1.13 1.12269756639010 0.00730243360990435 35 1.13 1.11928293574569 0.0107170642543128 36 1.13 1.12899913323122 0.00100086676878486 37 1.14 1.13363398044234 0.00636601955766403 38 1.14 1.14851971336284 -0.00851971336284119 39 1.14 1.13134923909717 0.00865076090282546 40 1.15 1.13722550914256 0.0127744908574350 41 1.15 1.15110383290820 -0.0011038329081976 42 1.15 1.157903858618 -0.00790385861799914 43 1.15 1.14447910843276 0.00552089156723912 44 1.15 1.15735536166582 -0.00735536166582418 45 1.15 1.15029325727767 -0.000293257277665715 46 1.14 1.14468011981976 -0.00468011981976502 47 1.14 1.13341384998283 0.00658615001717289 48 1.14 1.13745961607160 0.00254038392840372 49 1.13 1.14472190290522 -0.0147219029052230 50 1.12 1.14017835130926 -0.0201783513092593 51 1.13 1.11933419996396 0.0106658000360418 52 1.13 1.12776832855510 0.00223167144489578 53 1.13 1.13017313118788 -0.000173131187879427 54 1.12 1.13567042413462 -0.0156704241346211 55 1.13 1.12038391103486 0.00961608896514443 56 1.12 1.13257970368752 -0.0125797036875179 57 1.12 1.12366297890352 -0.00366297890352074 58 1.11 1.11456355510224 -0.00456355510224449 59 1.11 1.10658933531913 0.00341066468087248 60 1.11 1.10726948777243 0.00273051222757403 61 1.11 1.10987300577092 0.000126994229077804 62 1.14 1.11444821213015 0.0255517878698479 63 1.15 1.13525145023511 0.0147485497648880 64 1.15 1.14430665329922 0.00569334670078137 65 1.16 1.1485638636461 0.0114361363539004 66 1.15 1.15821315319504 -0.00821315319504445 67 1.16 1.15535127537210 0.00464872462790256 68 1.13 1.15779664287646 -0.0277966428764622 69 1.13 1.14033104205929 -0.0103310420592868 70 1.12 1.12606722013088 -0.00606722013088334 71 1.12 1.11916445746491 0.000835542535094325 72 1.11 1.1177711839068 -0.00777118390680109 73 1.11 1.11204217192436 -0.00204217192435752 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 1.12191821419247 1.10299059670871 1.14084583167623 75 1.12119441145808 1.09784095807567 1.1445478648405 76 1.11716278000427 1.09005252797542 1.14427303203312 77 1.11879717689371 1.08847385334689 1.14912050044054 78 1.11488681835827 1.08147052894156 1.14830310777497 79 1.12130895194151 1.08540744069127 1.15721046319175 80 1.11166820288119 1.07303848062653 1.15029792513584 81 1.11902164755691 1.07818479112559 1.15985850398823 82 1.11347034381342 1.07040632114199 1.15653436648485 83 1.11286770464936 1.06781375268351 1.15792165661520 84 1.10852145964969 1.06136951388195 1.15567340541742 85 1.11 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119146949n46bgk44o210o5/1ffjr1211914628.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119146949n46bgk44o210o5/1ffjr1211914628.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119146949n46bgk44o210o5/2i0a31211914628.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119146949n46bgk44o210o5/2i0a31211914628.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119146949n46bgk44o210o5/3cfs81211914628.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119146949n46bgk44o210o5/3cfs81211914628.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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